Urcohomologies and cohomologies of N-complexes

Hiramatsu, Naoya; Kato, Goro C.

doi:10.4171/PM/1875

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Portugaliae Mathematica

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Volume 67, Issue 4, 2010, pp. 511–524

DOI: 10.4171/PM/1875

Published online: 2010-11-24

Urcohomologies and cohomologies of N-complexes

Naoya Hiramatsu^[1] and Goro C. Kato^[2]

(1) Okayama University, Japan
(2) California Polytechnic State University, San Luis Obispo, USA

For a general sequence of objects and morphisms, we construct two N-complexes. Then we can define cohomologies (i, k)-type of the N-complexes not only on a diagonal region but also in the triangular region. We obtain an invariant defined on a general sequence of objects and morphisms. For a short exact sequence of N-complexes, we get the associated long exact sequence generalizing the classical long exact sequence. Lastly, several properties of the vanishing cohomologies of N-complexes are given.

Keywords: N-complex, N-exactness, complexifying functor, urcohomology

Hiramatsu Naoya, Kato Goro: Urcohomologies and cohomologies of N-complexes. Port. Math. 67 (2010), 511-524. doi: 10.4171/PM/1875